Laboratory measurements on the elastic moduli and the acoustic attenuation of fluid‐saturated porous rock cylinders are frequently affected by the boundary conditions of the rock sample, i.e., whether the curved surface of the cylindrical sample is exposed to air or properly sealed. In this paper, the analytical solutions of these problems for the extensional, torsional, and flexural modes are derived, and several numerical examples are computed. It was found that there exists an ‘‘artificial’’ attenuation caused by the open‐pore boundary condition, whose relaxation frequency, in the case of extensional mode, is directly proportional to the permeability of the rock and inversely proportional to the viscosity of the pore fluid and the square of the sample radius. This attenuation exists in both the extensional and the flexural modes but not in the torsional mode.